WASHINGTON (AP) — President Barack Obama’s first budget of his new term is a political straddle, aimed at enticing Republicans into a new round of deficit negotiations while trying to keep faith with Democrats who favor higher taxes in service of more government spending.

That gives everyone something to dislike if they are so inclined — and many in divided government are.

Obama’s stated goal is otherwise, namely that his $3.8 trillion budget should lead to the completion of a slow-motion grand deficit-cutting bargain by offering to save billions from programs previously sheltered from cuts. Medicare, Social Security and even military retirement are among them.

Perhaps to reassure Democrats unsettled by this approach, the president said his offer to trim future benefit increases for tens of millions of people is “less than optimal” and acceptable only if Republicans simultaneously agree to raise taxes on the wealthy and some businesses.

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“If anyone thinks I’ll finish the job of deficit reduction on the backs of middle-class families or through spending cuts alone that actually hurt our economy short-term, they should think again,” he said in an appearance Wednesday in the White House’s Rose Garden.

In rhetoric reminiscent of last year’s campaign, he added, “When it comes to deficit reduction, I’ve already met Republicans more than halfway.”

That’s not how they see it, and the issue was doubtless on the menu at the dinner for a dozen Republican senators that the president invited to the White House several hours later.

The early public reaction from Republicans was generally predictable, and none too positive.

House Speaker John Boehner, R-Ohio, said the president deserves “some credit for some of the incremental entitlement reforms that he has outlined in his budget.

“But I would hope that he would not hold hostage these modest reforms for his demand for bigger tax hikes,” Congress’ top Republican added, a repudiation of Obama’s insistence on higher taxes.

Senate Republican leader Mitch McConnell wasn’t nearly as generous. “We need a balanced budget that encourages growth and job creation. We don’t need an extreme, unbalanced budget that won’t balance in your lifetime or mine,” he said. He stopped short, barely, of accusing Obama of trying to blow up chances for compromise rather than improve them.

Overall, Obama’s budget accentuated the vast differences between Democrats and Republicans in their approaches to igniting a slow-growth economy — the issue that the president said was “the driving force behind every decision that I make.”

He proposed slowing the growth of federal deficits without eliminating them, and is seeking $1 trillion in higher taxes over a decade. His plan wipes out roughly $1 trillion in across-the-board spending cuts contained in legislation he signed more than a year ago and calls for new spending to expand pre-K programs and increase highway and mass transit construction and repair. The net impact on the deficit is savings of roughly $600 billion over a decade, far less than the $1.8 trillion the White House claimed.

By contrast, the budget that Republicans pushed through the House last month leaves across-the-board cuts in place, reduces spending by an additional $5.6 trillion over a decade and shows a balanced budget without raising taxes.

Both sides also express support for an overhaul of the tax code, although neither has yet fully staked out a position.

That makes benefit programs the likeliest — possibly the only — fruitful area for another deficit-reduction compromise in the coming months.

Over a decade, the president’s proposal to change the way the government calculates inflation — and therefore makes annual adjustments in benefits and income tax brackets — would produce savings estimated at $230 billion.

That’s a relatively small amount of savings in a decade, when overall spending will be counted in the tens of trillions of dollars.

Ironically, in political terms, it may be enough to do what Republicans have so far failed to accomplish — produce serious cracks in the unity that Democrats have generally maintained in earlier deficit-cutting negotiations.

Rep. Ed Markey, a Massachusetts Democrat running for the Senate, issued a statement saying he opposes the budget “because it would cut benefits to seniors on Social Security and makes other significant cuts to other key low-income programs that are vital to Massachusetts residents like low-income heating assistance.”

Democratic Sen. Barbara Mikulski of Maryland, who chairs the Senate Appropriations Committee, said in a statement that while she agrees with Obama on the need for a balanced approach, “there are specifics in the president’s plan around earned benefits about which I have serious concerns.”

Mary Kay Henry, president of the Service Employees International Union, a group with strong ties to Democrats, was more blunt. “We object to the president’s proposals to cut Social Security and Medicare. Social Security has never been contributing factor to the deficit and we cannot leave seniors out in the cold,” she said.

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EDITOR’S NOTE — David Espo is chief congressional correspondent for The Associated Press.